We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
Study challenges neural models in compositional learning tasks.
problem Challenges in neural models for compositional and relational learning.
method Introduced ConceptWorld environment for generating images from compositional concepts, tested various neural architectures.
result Neural models struggle with longer compositional chains and substitutivity tests.
New samplers improve compositional generation with diffusion models.
problem Improving compositional generation with diffusion models.
method Score-based interpretation, energy-based parameterization, Metropolis-corrected samplers.
result New samplers enable successful compositional generation across various tasks.
NeSS combines neural and symbolic approaches for better compositional generalization.
problem Lack of compositional generalization in deep learning models.
method NeSS uses a neural network to generate traces, executed by a symbolic stack machine with sequence manipulation.
result Achieves 100% generalization performance across multiple domains.
Paper analyzes stability and generalization of SCO algorithms.
problem Understanding how SCO algorithms perform on unseen data.
method Algorithmic stability analysis in statistical learning theory.
result Derives dimension-independent excess risk bounds for SCGD and SCSC.
We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory Units (Tree-SMU) to enable strong compositional generalization. Tree-SMU is a recurs…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all tasks -- both have difficulty with such generalization because they do not leve…
SCL discovers compositional structures in analogical reasoning tasks.
problem Discovering compositional structures in analogical reasoning tasks like Raven's Progressive Matrices.
method Proposes Scattering Compositional Learner (SCL) that composes neural networks in sequence.
result Achieves state-of-the-art performance on RPM datasets with significant improvements.
This paper proves hyperbolicity of virtual knot compositions.
problem Proving hyperbolicity of virtual knot compositions.
method Exploring the composition of hyperbolic virtual knots.
result Strong lower bounds on the volume of compositions.
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our framework, samples are generated by sampling components from component generators and fee…
New method to measure compositional generalization on realistic data.
problem Limited compositional generalization in machine learning.
method Maximizing compound divergence while ensuring small atom divergence.
result Machine learning architectures fail to generalize compositionally.
CFA improves model's ability to generalize across unseen domain-class combinations.
problem Challenges in real-world machine learning applications due to data distribution shifts and limited training data.
method Developed Compositional Feature Alignment (CFA) technique to improve CG ability of pretrained models.
result CFA outperforms common finetuning techniques in compositional generalization.
I consider how to influence CycleGAN, image-to-image translation, by using additional constraints from a neural network trained on art composition attributes. I show how I trained the the Art Composition Attributes Network (ACAN) by incorporating domain knowledge based on the rules of art evaluation and the result of a…
This work investigates the framework and performance issues of the composite neural network, which is composed of a collection of pre-trained and non-instantiated neural network models connected as a rooted directed acyclic graph for solving complicated applications. A pre-trained neural network model is generally well…
New findings show disentangled latent representations are not enough for robust compositional generalization.
problem Deep learning models struggle with compositional generalization, especially in out-of-distribution samples.
method Investigated a 2D Gaussian generation task with fully disentangled inputs, then forced disentangled latent representations into full-dimensional output space.
result Forcing disentangled latent representations into full-dimensional output space enables robust compositional generalization.
The study reveals simplicity bias in neural networks leading to better compositional mappings.
problem Understanding when and how to encourage neural networks to learn compositional mappings.
method Examined compositional mappings through coding length and gradient descent dynamics.
result Neural networks tend to learn the simplest bijections, explaining their good generalization.
New algorithm reduces complexity for optimizing complex machine learning tasks.
problem Optimizing complex machine learning objectives like reinforcement learning and portfolio management.
method Developed SARAH-Compositional algorithm using Stochastic Recursive Gradient Descent.
result Achieved optimal IFO complexity bounds for stochastic compositional optimization.
Compositional structures between parts and objects are inherent in natural scenes. Modeling such compositional hierarchies via unsupervised learning can bring various benefits such as interpretability and transferability, which are important in many downstream tasks. In this paper, we propose the first deep latent vari…
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
Memorizing rare examples helps neural networks generalize better.
problem Improving generalization in deep learning models.
method Theoretical analysis and experiments on neural networks with composition capability.
result Memorizing rare examples can help neural networks make correct predictions on rare test examples.
CompVAE handles multi-ensemble data with compositional generative model.
problem Handling multi-ensemble data with control and generative models.
method Derived from Bayesian variational principles, CompVAE learns a latent representation leveraging observational and symbolic information.
result Supports compositional generative model enabling multi-ensemble operations.
This paper studies how knots combine using Alexander Polynomials.
problem How knots combine and their determinants behave.
method Basic knot theory, Alexander Polynomials, and composition techniques.
result Generalized solution for knot determinants in compositions.
New filters match advanced composition for adaptive privacy, with practical constants.
problem Limitations of existing adaptive composition methods.
method Constructed new filters and odometers that match advanced composition rates, including constants.
result Achieved fully adaptive privacy with practical filters and odometers.
Generative model improves scene graph prediction for rare compositions.
problem Challenges in inferring unseen or rare scene graph compositions.
method Synthesizing rare scene graphs by perturbing real ones, using conditional GANs.
result Marginal but consistent improvements in zero- and few-shot metrics.
This paper analyzes how diffusion models learn and generalize concepts.
problem Learning and generalizing concepts in compositional data-generating processes.
method Introduced a structured identity mapping (SIM) task to analyze neural network learning dynamics.
result SIM task captures key empirical observations on compositional generalization.
Energy-based models can generate complex images by combining simpler concepts.
problem Generating natural images that satisfy complex logical combinations of concepts.
method Energy-based models combine probability distributions of simpler concepts to generate compositions.
result Energy-based models can generate images that satisfy conjunctions, disjunctions, and negations of concepts.
Unified algorithm for minimizing composite functions with flexible design.
problem Minimizing composite functions with specific structural properties.
method Unified accelerated algorithm for complementary composite minimization.
result Near-optimal algorithms for various optimization problems.
Standard methods in deep learning for natural language processing fail to capture the compositional structure of human language that allows for systematic generalization outside of the training distribution. However, human learners readily generalize in this way, e.g. by applying known grammatical rules to novel words.…
Diffusion models learn hierarchical composition rules from data.
problem How many samples do generative models need to learn hierarchical composition rules?
method Theoretical and empirical investigation of diffusion models on probabilistic context-free grammars.
result Diffusion models learn hierarchical composition rules with sample complexity scaling polynomially with context size.
This research proves guarantees on sequence models' generalization to longer and novel sequences.
problem Generalization to longer sequences and novel token combinations in sequence models.
method Provable guarantees on length and compositional generalization for various sequence models.
result Limited capacity models achieve both length and compositional generalization with diverse training distributions.
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with explicit and implicit regularizations. Our claims are being established with several im…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
Algorithm samples composite logconcave densities efficiently.
problem Sampling from composite logconcave densities efficiently.
method Uses a restricted Gaussian oracle and gradient queries.
result Achieves strong total variation distance guarantees.
The paper defines functions that induce bounded composition operators on RKHSs with analytic positive definite functions.
problem Characterizing functions that induce bounded composition operators on RKHSs.
method Intrinsic properties of RKHSs and asymptotic properties of orthogonal polynomials.
result Only affine transforms can induce bounded composition operators in a large class of RKHSs.
In the domain of algorithmic music composition, machine learning-driven systems eliminate the need for carefully hand-crafting rules for composition. In particular, the capability of recurrent neural networks to learn complex temporal patterns lends itself well to the musical domain. Promising results have been observe…
Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
Unified framework for aligning and composing diffusion models to satisfy multiple constraints.
problem Improving quality and compliance of generated samples from diffusion models.
method Constrained optimization framework that unifies alignment and composition of diffusion models.
result Proposed framework effectively satisfies multiple constraints in image generation.
Unified tractability conditions for various compositional inference queries.
problem Analyzing tractability of probabilistic and causal inference queries.
method Algebraic perspective on circuits, focusing on semiring operators.
result Unified sufficient conditions for tractable composition of operators.
Generative Adversarial Networks (GANs) can produce images of remarkable complexity and realism but are generally structured to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different ob…
Deep networks learn sparse hierarchical features without CoD.
problem Overparameterized deep networks struggle with the curse of dimensionality.
method Norm-constrained neural networks for sparse compositional functions.
result Deep networks can learn sparse hierarchical features efficiently.
We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ…
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Study on deep neural networks using branching processes and Mehler's formula.
problem Understanding the mathematical role of activation functions in compositional neural networks.
method Connection between compositional kernels and branching processes via Mehler's formula; new random features algorithm.
result Explicit formulas for eigenvalues of compositional kernels quantify complexity.
The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
This paper improves neural network explanations by quantifying and visualizing semantic compositions.
problem Improving neural network explanations for natural language processing tasks.
method Proposes a formal way to quantify word and phrase importance, introduces SCD and SOC algorithms.
result Our algorithms outperform prior methods in explaining neural network predictions.
New method tackles composite optimization with error feedback.
problem Challenges in distributed machine learning training and message compression.
method Combines Dual Averaging with EControl for composite optimization.
result First strong convergence analysis for composite optimization with error feedback.